`is_tree()` decides whether a graph is a tree, and optionally returns a possible root vertex if the graph is a tree.

## Usage

``is_tree(graph, mode = c("out", "in", "all", "total"), details = FALSE)``

## Arguments

graph

An igraph graph object

mode

Whether to consider edge directions in a directed graph. ‘all’ ignores edge directions; ‘out’ requires edges to be oriented outwards from the root, ‘in’ requires edges to be oriented towards the root.

details

Whether to return only whether the graph is a tree (`FALSE`) or also a possible root (`TRUE`)

## Value

When `details` is `FALSE`, a logical value that indicates whether the graph is a tree. When `details` is `TRUE`, a named list with two entries:

res

Logical value that indicates whether the graph is a tree.

root

The root vertex of the tree; undefined if the graph is not a tree.

## Details

An undirected graph is a tree if it is connected and has no cycles. In the directed case, a possible additional requirement is that all edges are oriented away from a root (out-tree or arborescence) or all edges are oriented towards a root (in-tree or anti-arborescence). This test can be controlled using the mode parameter.

By convention, the null graph (i.e. the graph with no vertices) is considered not to be a tree.

Other trees: `is_forest()`, `make_from_prufer()`, `sample_spanning_tree()`, `to_prufer()`

## Examples

``````
g <- make_tree(7, 2)
is_tree(g)
#> [1] TRUE
is_tree(g, details = TRUE)
#> \$res
#> [1] TRUE
#>
#> \$root
#> + 1/7 vertex, from 0c2f03a:
#> [1] 1
#>

``````